With the given information we can conclude that triangles OPN and LMN are similar. Thus, the proportion between corresponding sides is equal, it means:
[tex]\frac{NO}{OL}=\frac{NP}{PM}[/tex]
In the figure we can see that NO=4.4 OL=3.6 NP=3.3 and PM=x.
Replace these values and solve for x as follows:
[tex]\begin{gathered} \frac{4.4}{3.6}=\frac{3.3}{x} \\ \text{Multiply both sides by x} \\ \frac{4.4}{3.6}\cdot x=\frac{3.3}{x}\cdot x \\ \text{Simplify} \\ \frac{4.4}{3.6}\cdot x=3.3 \\ \text{Multiply both sides by 3.6} \\ \frac{4.4}{3.6}\cdot3.6\cdot x=3.3\cdot3.6 \\ \text{Simplify} \\ 4.4x=11.88 \\ \text{Divide both sides by 4.4} \\ \frac{4.4x}{4.4}=\frac{11.88}{4.4} \\ \text{Simplify} \\ x=2.7 \end{gathered}[/tex]
Thus, x=2.7
